You must be 18 years old to get a credit card by yourself. You can be younger than that if an adult co-signs with you or adds you as an authorized user to their credit card. You can also get a prepaid card younger than age 18.
While you can legally get a credit card as young as age 18, you need to have your own steady source of income to qualify for a credit card. Unfortunately, a monthly allowance from your parents doesn't count. It's for your own good. You need to have steady, depending monthly income so you can pay back any charges you make on your credit card.